Trim the wax beans and cut crosswise into thirds. In a large pot fitted with a steamer basket, bring 1 inch water to a boil. Add the wax beans and edamame, cover and steam until both are tender-crisp, about 5 minutes. Drain, rinse with cold water and drain again.
Trim the green onions, then thinly slice on the diagonal, including the tender green tops.
In a large bowl, combine the steamed edamame and wax beans, green onions, tomatoes and basil. Toss to mix evenly.
In a small bowl, combine the vinegar, lime juice, honey and mustard. Whisk in the olive oil. Add the dressing to the vegetables and toss to coat. Season with the salt and pepper. Serve chilled or at room temperature.